Local mountain passes for semilinear elliptic problems in unbounded domains

1996 ◽  
Vol 4 (2) ◽  
pp. 121-137 ◽  
Author(s):  
Manuel del Pino ◽  
Patricio L. Felmer
Keyword(s):  
Elliptic Problems ◽  
Unbounded Domains ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic Problems

Existence and non-existence results for semilinear elliptic problems in unbounded domains

1982 ◽  
Vol 93 (1-2) ◽  
pp. 1-14 ◽  
Author(s):  
M. J. Esteban ◽  
P. L. Lions
Keyword(s):  
Elliptic Equations ◽  
Elliptic Problems ◽  
Unbounded Domains ◽  
Existence Results ◽  
Semilinear Elliptic Equations ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic Problems ◽  
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SynopsisIn this paper, we prove various existence and non-existence results for semilinear elliptic problems in unbounded domains. In particular we prove for general classes of unbounded domains that there exists no solution distinct from 0 offor any smooth f satisfying f(0) = 0. This result is obtained by the use of new identities that solutions of semilinear elliptic equations satisfy.

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